The long-term objective of this application is to develop physical models and mathematical tools for optimizing treatments of HIV with fusion-inhibiting therapies. Kinetic data of virion-receptor interactions will be used to quantitatively categorize HIV strains based on fusogenicity (in the presence of varying CD4 and CCR5 receptor surface concentrations). Assays for mixtures of HIV strains will be proposed. Specific aims include: (1) Developing chemical kinetic models for HIV virus envelope protein-cell receptor interactions and fusion rates. These models will be used to analyze kinetic measurements and estimate parameters used in within-host virus population models. (2) Developing statistical measures for categorizing strains based on kinetic binding and fusion data. Two approaches will be used: principal components analysis (PCA) and cluster analysis. PCA will be applied directly to the data to find the viral strains whose fusogenicities span a sufficient range in receptor/coreceptor (e.g., CD4/CCR5) concentrations. Kinetic models derived in Aim (1) will be used to represent the kinetic data in a cluster analysis. (3) Using the theory of branching processes and the information garnered from Aims (1) and (2) to develop and improve upon models of HIV evolution. Both deterministic and stochastic models will be studied. (4) Developing deterministic models for gene therapy (via modification of, e.g., CD4/CCR5 expression) to determine the efficacy of proposed stem cell gene therapies in the face of mutations. Deterministic viral population models will be coupled to the stochastic theories developed in Aim (3) to compute probabilities of emergence and extinction of low-concentration, gene therapy-resistant strains. The proposed research represents a systematic, quantitative approach to the basic study of HIV-receptor/coreceptor interactions, and will potentially aid in optimizing drug treatments and gene therapies.